I entered the following values into my Ti-84 calculator:
stdDev({4.971e-2, 4.943e-2, 4.932e-2})
The answer was 2.0108.
Given ‘s’ is standard deviation, when I do it ‘longhand’:
s = sqrt(((4.971e-2 + 4.943e-2 + 4.932e-2)^2)/(3-1)), I get 0.104977
Is stdDev on the calculator RELATIVE standard deviation?
You need to subtract off the mean then square each difference from the mean and add not square the sum
The answer might divided by 3 rather than 2 if it is calculating the population standard deviation rather than estimating from a sample standard deviation. dividing by 3 also gives the maximum likelihood estimate in a sample, though that is less used.
The answers are 0.000201 and 0.000164.
I cannot fathom at all what the calculator is doing.
I don’t think you’re calculating stddev right. It’s the deep breath square root of the sum of the square of the differences between each data point and the mean divided by the number of elements.
mean(4.971e-2, 4.943e-2, 4.932e-2) = 4.949e-2
So stddev(4.971e-2, 4.943e-2, 4.932e-2) = sqrt( ((4.971e-2 - 4.949e-2)[sup]2[/sup] + (4.943e-2 - 4.949e-2)[sup]2[/sup] + (4.932e-2 - 4.949e-2)[sup]2[/sup])/3 )
Actually I checked and the sample std deviation is 0.000201, so I guess you’re just misreading the calculator’s decimal point position.
According to the printout I have (modified format for posting):
This is troubling, because when I use stdDev on the calculator:
stdDev({2.5610^-4,2.1610^-4 ,0.020*10^-4})
I get .0001366 and not 0.0154.
When I do sqrt(((2.56e-4+2.16e-4+.020e-4)^2)/(3-1)) I get .0003352.
So in short:
[ul][li]When I use the stdDev function as I was shown how to use it, and using the given values (as opposed to the numbers in the OP), the answer is not the given answer.[/li][li]When I take the square root of the sum of the values squared and divided by 2, I don’t get the given answer.[/ul][/li]
Even using a given example, stdDev and doing it ‘longhand’ both do not give the given answer.
That handout is wrong (and incidentally, so was my answer, I used the population stddev, not the sample one). It’s squaring the wrong quantity. You don’t square the sum. you sum the squares. For 3 values, a,b, and c, and mean m, the sample stddev is:
sqrt( ((a-m)^2 + (b-m)^2 + (c-m)^2)) / 2 )
OK, using that equation I get 0.0001366 – which is what the stdDev function gave me.
So it looks like stdDev is standard deviation, and not relative standard deviation.
Too late to edit:
The example says s = sqrt((2.5610^-4 + 2.1610^-4 + 0.020*10^-4) g^2 / (3-1)) = 0.0154 g.
As I said, I used the sum of the squares instead of the square of the sums to get the same answer I got by using the stdDev function on the calculator. The numbers given in the example are (x[sub]i[/sub] minus x-bar) squared. So in actuality, s = sqrt((2.5610^-4 + 2.1610^-4 + 0.020*10^-4) g^2 / (3-1)) is right because the numbers are all squares.
So where did the 0.0154 come from? I tried doing the manual calculation without squaring the sum of the squares, and came up with that.